Simplify Square Root of 762

What is the square root of 762 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√762 = A√B

Unfortunately, the square root of 762 cannot be simplified. Thus, here is the answer to the square root of 762 in its simplest form:

√ 762 = √ 762

Here are two different methods we used to determine why the square root of 762 cannot be simplified.

1) To be able to simplify the square root of 762, one of the factors of 762 other than 1 must be a perfect square. The factors of 762 are 1, 2, 3, 6, 127, 254, 381, and 762. Since none of these factors are perfect squares, the square root of 762 cannot be simplified.

2) To be able to simplify the square root of 762, all the prime factors of 762 cannot be unique. When we did prime factorization of 762, we found that 2 x 3 x 127 equals 762. Since all the prime factors are unique, the square root of 762 cannot be simplified.

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